ddml_plm() R function from [ddml]

Estimator for the Partially Linear Model.

Estimator for the partially linear model.


ddml_plm(
  y,
  D,
  X,
  learners,
  learners_DX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  cluster_variable = seq_along(y),
  subsamples = NULL,
  cv_subsamples_list = NULL,
  silent = FALSE
)

Arguments

y: The outcome variable.
D: A matrix of endogenous variables.
X: A (sparse) matrix of control variables.
learners: May take one of two forms, depending on whether a single learner or stacking with multiple learners is used for estimation of the conditional expectation functions. If a single learner is used, learners is a list with two named elements:
- what The base learner function. The function must be such that it predicts a named input y using a named input X.
- args Optional arguments to be passed to what.
If stacking with multiple learners is used, learners is a list of lists, each containing four named elements:
- fun The base learner function. The function must be such that it predicts a named input y using a named input X.
- args Optional arguments to be passed to fun.
- assign_X An optional vector of column indices corresponding to control variables in X that are passed to the base learner.
Omission of the args element results in default arguments being used in fun. Omission of assign_X results in inclusion of all variables in X.
learners_DX: Optional argument to allow for different estimators of $E[D|X]$ . Setup is identical to learners.
sample_folds: Number of cross-fitting folds.
ensemble_type: Ensemble method to combine base learners into final estimate of the conditional expectation functions. Possible values are:
- "nnls" Non-negative least squares.
- "nnls1" Non-negative least squares with the constraint that all weights sum to one.
- "singlebest" Select base learner with minimum MSPE.
- "ols" Ordinary least squares.
- "average" Simple average over base learners.
Multiple ensemble types may be passed as a vector of strings.
shortstack: Boolean to use short-stacking.
cv_folds: Number of folds used for cross-validation in ensemble construction.
custom_ensemble_weights: A numerical matrix with user-specified ensemble weights. Each column corresponds to a custom ensemble specification, each row corresponds to a base learner in learners

(in chronological order). Optional column names are used to name the estimation results corresponding the custom ensemble specification.
custom_ensemble_weights_DX: Optional argument to allow for different custom ensemble weights for learners_DX. Setup is identical to custom_ensemble_weights. Note: custom_ensemble_weights and custom_ensemble_weights_DX must have the same number of columns.
cluster_variable: A vector of cluster indices.
subsamples: List of vectors with sample indices for cross-fitting.
cv_subsamples_list: List of lists, each corresponding to a subsample containing vectors with subsample indices for cross-validation.
silent: Boolean to silence estimation updates.

Returns

ddml_plm returns an object of S3 class ddml_plm. An object of class ddml_plm is a list containing the following components:

coef: A vector with the $\theta_0$ estimates.
weights: A list of matrices, providing the weight assigned to each base learner (in chronological order) by the ensemble procedure.
mspe: A list of matrices, providing the MSPE of each base learner (in chronological order) computed by the cross-validation step in the ensemble construction.
ols_fit: Object of class lm from the second stage regression of $Y - \hat{E}[Y|X]$ on $D - \hat{E}[D|X]$ .
learners,learners_DX,cluster_variable, subsamples, cv_subsamples_list, ensemble_type: Pass-through of selected user-provided arguments. See above.

Details

ddml_plm provides a double/debiased machine learning estimator for the parameter of interest $\theta_0$ in the partially linear model given by

$Y = \theta_0D + g_0(X) + U,$

where $(Y, D, X, U)$ is a random vector such that $E[Cov(U, D\vert X)] = 0$ and $E[Var(D\vert X)] \neq 0$ , and $g_0$ is an unknown nuisance function.

Examples


# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the partially linear model using a single base learner, ridge.
plm_fit <- ddml_plm(y, D, X,
                    learners = list(what = mdl_glmnet,
                                    args = list(alpha = 0)),
                    sample_folds = 2,
                    silent = TRUE)
summary(plm_fit)

# Estimate the partially linear model using short-stacking with base learners
#     ols, lasso, and ridge. We can also use custom_ensemble_weights
#     to estimate the ATE using every individual base learner.
weights_everylearner <- diag(1, 3)
colnames(weights_everylearner) <- c("mdl:ols", "mdl:lasso", "mdl:ridge")
plm_fit <- ddml_plm(y, D, X,
                    learners = list(list(fun = ols),
                                    list(fun = mdl_glmnet),
                                    list(fun = mdl_glmnet,
                                         args = list(alpha = 0))),
                    ensemble_type = 'nnls',
                    custom_ensemble_weights = weights_everylearner,
                    shortstack = TRUE,
                    sample_folds = 2,
                    silent = TRUE)
summary(plm_fit)

References

Ahrens A, Hansen C B, Schaffer M E, Wiemann T (2023). "ddml: Double/debiased machine learning in Stata." https://arxiv.org/abs/2301.09397

Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C B, Newey W, Robins J (2018). "Double/debiased machine learning for treatment and structural parameters." The Econometrics Journal, 21(1), C1-C68.

Wolpert D H (1992). "Stacked generalization." Neural Networks, 5(2), 241-259.

ddml_plm function